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Cantilevers.

4-39

the section only, so here the shear ordinates are drawn downward
on the line a , and equal W in every case.

II. Cantilever with Uniformly Distributed Load (Fig. 395),
the load being represented by the weight of the beam. Con-
sidering the beam hinged successively at A, B, c, D, and E, the
loads on the right may be successively concentrated at their
middle points, and the Bending Moments become:

At A-

Wx-

4     ><S/    W/X32

W    /               r

At c=   x-   = W/x -     cc

24        8

W    /              i

At D =   x-   =W/x    a

48         32

= 32

i=i

and at E = nothing, as shewn by diagram, and as the ordinates
vary as the square of the abscissae at a If, the curve is a parabola
with b as vertex.

Shearing Force on right of section A = W, at section B =f W,

W  W
and at c D and E,  ,  , and nothing respectively, as shewn by

diagram on a^br

III. Girder with concentrated load at centre and ends merely

W
supported (Fig. 396).  Reactions will each equal  , which we

shall use in. estimating the moment. Htl balances Rt2 round W
as a pivot and the stress at E is due to one or the other, but

W
not to both.    Then calling each reactipn  the Bmding Moments

will be :

/
~
8

-7    a

Atc= 
2

W

2

W

 x~

22

8
/

-     a 2

 3

10

i

-     OCA

4

and similarly between j and E.